document.write( "Question 99771: 6. Find the choice below which gives a first step in solving the given system of equations by the addition method.
\n" ); document.write( "2x - 3y = 7\r
\n" ); document.write( "\n" ); document.write( "x - 4y = 2\r
\n" ); document.write( "\n" ); document.write( "(Points: 10)
\n" ); document.write( " Multiply the first equation by 3 and the second by 4.
\n" ); document.write( " Multiply the first equation by -4 and the second by -2.
\n" ); document.write( " Multiply the second equation by -2.
\n" ); document.write( " Multiply the first equation by 4. \n" ); document.write( "
Algebra.Com's Answer #72643 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Find the choice below which gives a first step in solving \r\n" );
document.write( "the given system of equations by the addition method. \r\n" );
document.write( "2x - 3y = 7 \r\n" );
document.write( " x - 4y = 2 \r\n" );
document.write( "(Points: 10)\r\n" );
document.write( "Multiply the first equation by 3 and the second by 4. \r\n" );
document.write( "Multiply the first equation by -4 and the second by -2. \r\n" );
document.write( "Multiply the second equation by -2. \r\n" );
document.write( "Multiply the first equation by 4.\r\n" );
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document.write( "Let's try the first choice:\r\n" );
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document.write( "Multiply the first equation by 3 and the second by 4.\r\n" );
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document.write( "2x - 3y = 7  becomes 6x -  9y = 21\r\n" );
document.write( " x - 4y = 2  becomes 4x - 16y = 8\r\n" );
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document.write( "Will the terms in x or y cancel if I add the two \r\n" );
document.write( "new equations and get a third new equation in only \r\n" );
document.write( "one letter? \r\n" );
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document.write( "No because when I add those two new equations:\r\n" );
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document.write( " 6x -  9y = 21\r\n" );
document.write( " 4x - 16y =  8\r\n" );
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document.write( "10x - 25y = 29\r\n" );
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document.write( "Nothing canceled out and the resulting equation still contains two \r\n" );
document.write( "variables, x and y, so the first choice is not correct.   \r\n" );
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document.write( "Now let's try the second choice:\r\n" );
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document.write( "Multiply the first equation by -4 and the second by -2.\r\n" );
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document.write( "2x - 3y = 7  becomes -8x + 12y = -28\r\n" );
document.write( " x - 4y = 2  becomes -2x +  8y =  -4\r\n" );
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document.write( "Will the terms in x or y cancel if I add the two \r\n" );
document.write( "new equations and get a third new equation in only \r\n" );
document.write( "one letter? \r\n" );
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document.write( "No because when I add those two new equations:\r\n" );
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document.write( " -8x + 12y = -28\r\n" );
document.write( " -2x -  8y =  -4\r\n" );
document.write( "----------------\r\n" );
document.write( "-10x +  4y = -32\r\n" );
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document.write( "Nothing canceled out and the resulting equation still contains\r\n" );
document.write( "two variables, x and y, so the second choice is not correct \r\n" );
document.write( "either. \r\n" );
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document.write( "---------------\r\n" );
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document.write( "Let's try the fourth choice:\r\n" );
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document.write( "Multiply the first equation by 4. Note: Nothing was said in this\r\n" );
document.write( "choice about multiplying the second at all, so that is to be \r\n" );
document.write( "interpreted as leaving the second equation just as it is, or\r\n" );
document.write( "multiplying it by 1.  \r\n" );
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document.write( "2x - 3y = 7  becomes   8x - 12y = 28\r\n" );
document.write( " x - 4y = 2  stays as   x -  4y =  2\r\n" );
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document.write( "Will the terms in x or y cancel if I add the two \r\n" );
document.write( "new equations and get a third new equation in only \r\n" );
document.write( "one letter? \r\n" );
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document.write( "No because when I add those new first equation to the old\r\n" );
document.write( "second equation:\r\n" );
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document.write( "  8x - 12y = 28\r\n" );
document.write( "   x -  4y =  2\r\n" );
document.write( "----------------\r\n" );
document.write( "  9x - 16y = 30\r\n" );
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document.write( "nothing canceled out and the resulting equation still contains \r\n" );
document.write( "two variables, x and y, so the fourth choice is not correct either. \r\n" );
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document.write( "Let's try the third choice:\r\n" );
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document.write( "Multiply the second equation by -2. \r\n" );
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document.write( "Note: Nothing was said in this choice about multiplying the first\r\n" );
document.write( "at all, so that is to be interpreted as leaving the first equation\r\n" );
document.write( "just as it is, or you could say, multiplying it by 1.  \r\n" );
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document.write( "2x - 3y = 7  stays as  2x - 3y =  7\r\n" );
document.write( " x - 4y = 2  becomes  -2x + 8y = -4\r\n" );
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document.write( "Will the terms in x cancel if I add the old first equation\r\n" );
document.write( "to the new second equation and get a third new equation in \r\n" );
document.write( "only one letter? \r\n" );
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document.write( "YES INDEED! Because when I add the old first equation to the new\r\n" );
document.write( "second equation:\r\n" );
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document.write( "  2x - 3y =  7\r\n" );
document.write( " -2x + 8y = -4\r\n" );
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document.write( "     - 5y =  3\r\n" );
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document.write( "The 2x and the -2x canceled out and the result is an equation\r\n" );
document.write( "in just ONE variable y, so the third choice is INDEED the correct\r\n" );
document.write( "choice.\r\n" );
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document.write( "Edwin

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